AI 中文总结
该研究针对自适应光学系统相互作用矩阵的校准难题，提出基于加权最小二乘拟合的仿射模型校准方法，将其应用于THEMIS太阳望远镜AO系统，发现简单差值法性能最优且实现简便。
AI 中文摘要
相互作用矩阵将可变形反射镜（DM）指令的效应对波前传感器（WFS）的感知进行建模，是自适应光学（AO）控制的基石。该矩阵的校准难点源于AO系统的自由度数量、非线性特性及时间演化。本文考虑DM指令与WFS测量值之间未知映射的仿射近似，通过以加权最小二乘意义拟合向DM发送随机探测指令获取的WFS数据，得到该仿射模型参数的最优估计量。根据模型是直接拟合WFS数据还是拟合连续WFS数据的差值，可采用多种校准方法。我们推导了模型各分量估计量的闭式表达式。所提校准方法可在不同条件下应用：观测前、内部光源上，或开环、闭环的天空观测中。通过引入遗忘因子以降低数据随时间的权重，我们证明该模型可利用简单递推规则持续学习，这些规则的低计算复杂度使其适用于与AO回路相同频率的实时处理。我们推导了所提估计量均方误差（MSE）的简单表达式，并将所提校准方法应用于THEMIS太阳望远镜AO系统的真实遥测数据。结果表明，简单差值法是首选方法：不仅能产生MSE最小的估计量，且与AO系统中广泛使用的推拉法相比，实现方式极为简单。
英文摘要
The interaction matrix models the effects of deformable mirror (DM) commands as perceived by the wavefront sensor (WFS) and is the cornerstone of the Adaptive Optics (AO) control. Difficulties to calibrate this matrix arise due to the number of degrees of freedom, the non-linearity, and temporal evolution of the AO system. An affine approximation of the unknown mapping between the DM commands and the WFS measurements is considered. Optimal estimators of the parameters of this affine model are obtained by fitting, in the weighted least squares sense, WFS data acquired with random probe commands sent to the DM. Several calibration methods are being considered depending on whether the model is directly fit to the WFS data or to the differences between successive WFS data. We derive closed-form expressions of the estimators of the components of the model. The proposed calibration methods can be applied under different conditions: before observing, on an internal source, or on-sky in open- or closed-loop. By introducing forgetting factors to reduce the weight of data as they age, we show that the model can be learned continuously using simple recurrence rules. The low computational complexity of these rules makes them suitable for real-time at the same frequency as the AO loop. We derive simple expressions for the mean squared errors (MSE) of the proposed estimators. We apply the proposed calibration methods to real telemetry data from the AO system of the THEMIS solar telescope. Our results show that the simple differences method is the method of choice: not only does it produce estimators with the least MSE, but it is also very simple to implement compared to the push-pull method which is widely used in AO systems.
